June 09, 2009

Junk Math and the BMI Charade

Posted by Milos Sugovic

Numbers are our best friend, unless of course, they’re used irresponsibly. The BMI or body mass index is one of the most widely used (or misused) mathematical formulas out there. Why? Because it’s a formula that generates a magic number which is scientific, accurate, and easy to understand. And like most formulas, it plays a key role in decision-making. Too bad it’s complete garbage.

Nowadays, there’s a formula or index for virtually everything out there, and like the BMI, claims accuracy beyond its statistical power. Unfortunately, the PR industry, one that has traditionally struggled with quantifying qualitative data, isn’t immune to this predisposition. So it’s important for all of us to approach “diagnostic” measures, like the BMI, with a critical eye.

One doesn’t need a course in multivariate calculus to understand why the BMI measure is nonsense. Just look at the infamous formula:

BMI = weight in pounds / (height in inches x height in inches) x 703

First of all, it leaves out measures such as waist size, as well as the importance of relative densities of muscle, bone, and fat. But let’s ignore those for a minute and assume they’re irrelevant for the sake of simplicity. Just look at the formula. Why is height in inches squared? Is there any scientific reasoning behind squaring one’s height? What about the random 703? Where did that come from?

To answer all this, let’s look to the founder of the BMI, a Belgian mathematician, statistician, and sociologist known as Adolphe Quetelet (1796 - 1874). Quetelet was interested in understanding the “average man” and in the course used statistical methods to identify mathematical formulas that would correlate, numerically, with the average citizen. Given that Quetelet was working with metric units, we know that the 703 is a constant used to convert metric units to imperial units - I can live with that.

The height squared, on the other hand, plays no scientific role apart from establishing a “goodness of fit” – in statistical speak - between the data and the model. Nothing more, nothing less. Look at it this way: if I gave you the numbers 178, 189, 204 and 155, you can come up with an infinite set of simple formulas that will model that pattern accurately. Statisticians do it all the time, and Quetelet knew what he was doing – he was trying to draw conclusions about society as a whole and not at the individual level.

But many of us forget that. And before you know it, we - including the Center for Disease Control - start using formulas like the BMI as a diagnostic tool. In fact, the BMI measure is oftentimes used as a “trigger” for prescribing more exercise. Fine, no problem with that, but it seems we forget that most individuals put on muscle weight and reduce body fat as a result of exercise. That increases the numerator (weight in pounds) and one’s BMI, indicating that one is less healthy and needs to exercise more! What’s even more absurd is the fact that the more muscular an individual the higher the likelihood of “failing” the BMI test and being classified as obese.

So how can we trust and blindly use this measure as a prescriptive tool on an individual basis? The CDC, for one, admits that it’s used “because calculation requires only height and weight, it is inexpensive and easy to use for clinicians and for the general public.” Ahhhhh, so it’s a dollars game and has nothing to do with medical accuracy. Fair enough. But no need to sell it as a reliable indicator.

What bothers me most is that we find ourselves too often handing over reason in exchange for empirical reassurance and comfort. There’s nothing wrong with Quetelet’s BMI from a statistical modeling point of view, it’s how we use it that’s utterly erroneous. So before you look for ways to put all your eggs in one basket based on some index or percentage, ask yourself “What is being measured?” “How reliable is it?” and “Does the model fit my needs?”

There’s nothing more comforting than fully understanding the data you’re using and the models that can predict the underlying patters. Statistical methods play a differentiating role in many business decisions, and for better or worse, give recommendations credibility via empirics. But don’t believe numbers blindly. Misleading statistics are increasingly abundant and a degree of skepticism will ensure you’re not the fool that’s making business decisions based on a measure like the BMI.

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